Patrick Henry Community College

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1 Patrick Henry Community College MTH 167 PreCalculus with Trigonometry INSTRUCTOR: Shannon Harrell OFFICE LOCATION: PHCC West Hall, Room 323 OFFICE HOURS: M-F 12:30 3:00 P.M., or by appointment OFFICE PHONE: , extension 4 ADDRESS: sharrell@pgsmst.com CLASS MEETING TIME: M/W 9:25 10:55 a.m.; T/Th 9:25 10:55 a.m. CLASSROOM LOCATION: PHCC West Hall, Room 124 COURSE CREDITS: 5 PREREQUISITE(S): Prerequisite: Competency in Math Essentials MTE 1-9 as demonstrated through the placement and diagnostic tests, or by satisfactorily completing the required MTE units or equivalent. COURSE DESCRIPTION This is an advanced PreCalculus course that includes the study of algebraic functions such as, linear, quadratic, cubic, logarithmic, exponential, polynomial, rational, trigonometric, and inverse trigonometric functions. Other topics include vectors, matrices, partial fraction decomposition, conics, sequences, series, and introductory calculus topics of limits and derivatives. The course will build on the concepts learned in previous math courses and prepare students for the higher levels of mathematics. The diversity of topics and versatility of the knowledge gained in this course will enable students to solve problems in many fields of study. Mathematics at the Governor s School provides students with a unique opportunity to investigate and discover many types of functions, their characteristics, and model real life applications using the graphs of various functions. The 4-prong approach is utilized, encouraging students to focus on concepts when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. An emphasis will be placed on preparing students to use mathematics to problem solve, promote critical thinking, and solve higher-level problems while developing underlying calculus concepts. Technological equipment is used to enhance understanding of concepts, and confirm and analyze solutions found algebraically. COURSE INTRODUCTION This course begins with an in-depth study of algebraic concepts and their application. The study of trigonometry is a large focus of this course. Trigonometry was developed for astronomy and geography; it is also used in physics, engineering, and chemistry. It is used primarily in calculus, thus a solid foundation is essential for success in that and future math courses. The material covered in this course is intended to prepare the student for their future mathematic endeavors. A. COURSE OBJECTIVES Upon successful completion of this course, the student should: Ø Develop effective study skills in order to master course content and objectives. Ø Demonstrate an understanding of the basic mathematical skills used in applied pre-calculus. Ø Communicate clearly and effectively mathematical principles using proper vocabulary. Ø Apply the principles and concepts of pre-calculus to solve practical problems in mathematics. Content Covered I. Relations and Functions a. Distinguish between relations and functions. b. Evaluate functions both numerically and algebraically. c. Determine the domain and range of functions in general, including root and rational functions. 1

2 d. Perform arithmetic operations on functions, including the composition of functions and the difference quotient. e. Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations. f. Determine and verify inverses of one-to-one functions. II. Polynomial and Rational Functions a. Determine the general and standard forms of quadratic functions. b. Use formula and completing the square methods to determine the standard form of a quadratic function. c. Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions. d. Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph. e. Determine if a function demonstrates even or odd symmetry. f. Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers. g. Identify intercepts, end behavior, and asymptotes of rational functions, and graph. h. Solve polynomial and rational inequalities. i. Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x)) j. Decompose partial fractions of the form P(x)/Q(x) where Q(x) is a product of linear factors. III. Exponential and Logarithmic Functions a. Identify and graph exponential and logarithmic functions and their transformations. b. Use properties of logarithms to simplify and expand logarithmic expressions. c. Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms. d. Solve exponential and logarithmic equations using one-to-one and inverse properties. e. Solve application problems involving exponential and logarithmic functions. IV. Systems of Equations a. Solve three variable linear systems of equations using the Gaussian elimination method. V. Trigonometric Functions a. Identify angles in standard form in both degree and radian format and convert from one to the other. b. Find the arc length. c. Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry. d. Use reference angles to evaluate trig functions. e. Find the value of trigonometric functions of angles using a calculator. f. Use fundamental trigonometric identities to simplify trigonometric expressions. g. Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts. h. Use trig functions to model applications in the life and natural sciences. VI. Analytic Trigonometry a. Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities. b. Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions. c. Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions. d. Solve trigonometric equations over restricted and non-restricted domains. VII. Applications of Trigonometry a. Solve right triangles and applications involving right triangles. b. Use the Law of Sines and Cosines to solve oblique triangles and applications. c. Apply concepts of trigonometry to extended topics such as plotting polar coordinates, 2

3 VIII. Conics converting rectangular and polar coordinates from one to the other, identifying vector magnitude and direction, or performing operations with vectors such as addition, scalar multiplication, component form, and dot product. a. Identify the conic sections of the form: Ax 2 + By 2 + Dx + Ey + F = 0. b. Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin. c. Identify essential characteristics unique to each conic. d. Graph equations in conic sections, centered both at the origin and not at the origin. e. Solve applications involving conic sections. B. VCCS CORE COMPETENCIES Degree graduates will demonstrate the ability to 1.1 Understand and interpret complex materials; 2.6 Use problem solving skills; 4.1 Determine the nature and extent of the information needed; 4.2 Access needed information effectively and efficiently; 6.1 Use logical and mathematical reasoning within the context of various disciplines; 6.2 Interpret and use mathematical formulas; 6.3 Interpret mathematical models such as graphs, tables and schematics and draw inferences from them; 6.4 Use graphical, symbolic, and numerical methods to analyze, organize, and interpret data; 6.5 Estimate and consider answers to mathematical problems in order to determine reasonableness; and 6.6 Represent mathematical information numerically, symbolically, and visually, using graphs and charts. C. METHOD OF INSTRUCTION A variety of instructional methods will be utilized throughout this course. Students will be introduced to the mathematical concepts in the classroom via lecture, cooperative learning, and exploration. As a group we will work extensively on study habits, appropriate use of the graphing calculators, and student communication both oral and written. Students will be encouraged to actively participate in the learning process to help ensure that they understand the material. Many examples will be provided through lecture and class activities. The use of , Google websites, and Blackboard is essential. D. TEXTBOOK(S) AND REQUIRED TOOLS OR SUPPLIES PreCalculus Fourth Edition J. Douglas Faires, James DeFranza Thomson Learning Inc., 2007 Pencils Notebook loose-leaf paper (lots!) Graph paper (lots!) Three-ring binder, 2 3 Dividers for three-ring binder (one set with 6 tabs labeled notes, homework, quizzes, tests, free response questions (FRQs), and projects) Graphing calculator E. STUDENT EVALUATION Grades will be based on the following: Homework: 20% This grade is based on daily checks for completion. Homework should be kept in a three-ring binder, and should be organized chronologically by date with the page number of the assignment included at the top of the page. Homework will not be accepted for a late grade if the student is present in class on the day it is due. Homework will be graded using the following rubric: 3

4 Score Criteria Assignment 90% or more completed before arriving to class. Full work and solutions shown. 5 Questions written down when you are stuck on a problem. Assignment 80% or more completed before arriving to class. Full work and solutions shown. 4 Questions written down when you are stuck on a problem. Assignment 60% or more completed before arriving to class. Full work and solutions shown. 3 Questions written down when you are stuck on a problem. 2 Less than 60% of the problems attempted. 1 Less than 30% of the problems attempted. 0 No problems attempted. When you don t know how to solve a problem, you must make an attempt to start it and then write down specific questions you have about how to continue solving the problem. Just writing a question mark,?, or stating I don t know what to do will not get you credit for the problem. Examples of sentences you could write: Should I use the quadratic formula to find the solution(s) from this point? Should I use a double angle identity here? Free-response Questions (FRQs): 15% Free-response questions covering multiple concepts will be assigned throughout this course. Students should complete problems following the guidelines provided by the instructor. These assignments will be graded on a nine-point scale following the AP grading rubric and will be due by 7:45 a.m. on the due date. Papers will not be accepted after midnight of the due date; there are no exceptions. Papers submitted after 7:45 a.m., but before midnight, will incur a point deduction based on a pro-rated scale. Students should scan and the assignment to the instructor by 7:45 a.m. if he/she is not present at the Governor s School on the due date. Quizzes: 20% One or two closed-book quizzes will be given in each unit, usually covering two or three sections of the chapter. These quizzes will be announced. Tests: 45% A test will be given at the end of each unit. An exam will be given at the end of each semester and will count 25% of the semester grade. F. GRADING SCALE: A B C D F 59 below A student earning a grade of C or higher will earn college credit for this course. G. EXPECTATIONS FOR STUDENT SUCCESS Attendance Students should attend class daily; seven absences (excused or unexcused) will lower final college grade by one letter grade. Three tardies or three early dismissals will constitute one absence. Students should the instructor when missing a class to obtain any missed assignments, notes, etc. Students should see the instructor the day returning from a missed class to ask questions pertaining to the lecture and/or assignment. Students should make arrangements to make up any assessment that is missed due to absence. Students should submit a note to Mrs. East within 24 hours of the student s return with a valid reason for student s absence. No make-up work will be allowed for unexcused absences and any assignment for that day will receive a zero. 4

5 Submitting Work Students should submit all work by the due date. Assignments not submitted by the due date will incur a 25-point deduction per day after the due date. All assignments must be submitted electronically and should be turned in as one document, Microsoft Word or PDF. The document can contain multiple pages if necessary, however, it should not be multiple attachments. If multiple attachments are submitted then only the content in the first attachment will be graded. All assignments should be saved as last name_first initial_assignment name. Students should submit all work using the corresponding link in Blackboard (Bb). Each assignment will have its own link in Blackboard. o To submit assignments using Bb, click on the link for the assignment, then upload the file, preview the file to ensure that all portions or problems are present, then click the submit icon. Students should also upload projects and specified assignments on their Google website. Class Atmosphere Students should abide by all rules as outlined in the student handbook. Students may have drinks in the classroom, provided the drink has a screw-on cap. Students must leave their area clean. Students should show respect for classmates and the instructor, listen carefully, and not interrupt someone who is talking. Cell phones may not be used in class and must be placed on the silent mode setting before entering the classroom. All students will place their cell phones in the cell-phone holder each day upon entering the classroom. WHAT A STUDENT CAN EXPECT FROM THE INSTRUCTOR On any day that a student is absent from class, the lesson will be recorded and posted on Blackboard or ed to the student(s). The instructor will evaluate quizzes, tests, and other assignments promptly and will provide feedback. Grades will be posted on Blackboard within 10 days of the due date of the assignment. The instructor will be available before school by 7:30 A.M., between classes, and after governor s school for tutoring. Tutoring is available at other times by appointment. Please if you would like to set up a time to meet to work on specific questions or topics/concepts. Timely responses to s. I check my frequently each day, Monday Friday, until 9 p.m. to answer any questions about homework, assignment clarification, etc.; any sent after 9 p.m. will not be answered until the following day. I check my sporadically on Saturday and Sunday and will respond within 24 hours. Afternoon/evening study sessions will be scheduled throughout the year as needed. Continuous support, assistance, and encouragement. H. EMERGENCY INFORMATION In case of emergency students should exit the classroom, turn left and then turn left to exit the building through the automatic doors. Students should proceed quickly and quietly to the far end of the parking lot adjacent to Stone Hall. I. STUDENT SUPPORT/DISABILITY STATEMENT: Patrick Henry Community College makes every effort to accommodate individuals with disabilities for all programs, services, and activities available to the public. J. IMPORTANT DATES TO REMEMBER: The school calendar is available in the student handbook and at the following link: K. SPECIFIC COLLEGE POLICIES Academic Honesty Students are expected to abide by the code of conduct and academic integrity found in the student handbook. Students will be required to sign a pledge on any take-home quizzes/tests stating On my honor, I have neither given nor received aid on this assignment. Infractions of the honor code will not be tolerated and will be reported to the 5

6 director and will be addressed with the student and his/her parent(s)/guardian(s). All violations of academic integrity will also be reported to each student s honor organization. Inclement Weather If Henry County Schools are delayed one hour, Governor s School will open one hour late. One common question asked is If my base school is closed but roads in my residential area are clear, should I come to Governor s School? The decision to attend under those circumstances should be made by the parent(s)/guardian(s). If Henry County Schools are delayed two hours, Governor s School classes will be canceled. If Henry County Schools are closed, Governor s School is closed and classes do not meet. Henry County/Martinsville work days do not impact classes at Piedmont Governor s School. Assignments and/or lectures may be posted on Blackboard on days when Governor s School classes are affected by inclement weather. It is the student s responsibility to check Blackboard and complete the assignments before their next class meeting. L. Resources is an online tutoring service which gives students 24/7 access to highly qualified, experienced, and specially trained tutors. Virtual whiteboard technology lets students and tutors share the same screen. Students may submit writing assignments to be evaluated / proofread. All live sessions with tutors and submitted questions are saved so students can view or print them out. Any PHCC student can access Smarthinking free of charge. Smarthinking can only be accessed through BlackBoard. Further information may be obtained from your instructor or the Writing Center Tutors. Internet Resources 6

7 Patrick Henry Community College MTH 167 PreCalculus with Trigonometry INSTRUCTOR: Shannon Harrell M. AFFIDAVIT My signature below indicates that I have read and understand this syllabus. Student Name Student Signature Date Parent/Guardian Name Parent/Guardian Signature Date Note: This syllabus is subject to change at the discretion of the instructor. It is the responsibility of the student to keep abreast of these changes. This syllabus conforms to the Patrick Henry Community College syllabus guidelines. 7

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